{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RBNIM5BGQLTBANJP6ZI2AWSUZP","short_pith_number":"pith:RBNIM5BG","schema_version":"1.0","canonical_sha256":"885a86742682e610352ff651a05a54cbd0fb975b672d23b7b5423c0732fa7879","source":{"kind":"arxiv","id":"1412.2414","version":3},"attestation_state":"computed","paper":{"title":"Asymptotics of action variables near semi-toric singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Christophe Wacheux","submitted_at":"2014-12-07T23:34:53Z","abstract_excerpt":"The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does not apply. In particular, the affine structure of the image of the moment map around has non-trivial monodromy. In this article, we establish that the singular behaviour and the multi-valuedness of the Action integrals is given by a complex logarithm. This extends a previous result by Vu Ngoc to any dimension. We also calculate the monodromy m"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1412.2414","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2014-12-07T23:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"27eb6edb50600829b3d9de227187179dcabfa4c6631f2d5fdba50523fac55f16","abstract_canon_sha256":"0d949769f76210d1452eeea202d131f11c0c6aaf18f9d9f4e2e23eea412f4a40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:02.492586Z","signature_b64":"38VTsYVwF9sTVd08eZQl/Lj9PEhLUJvAGKxui5SUgXFbJKzGrQrDoJkBj1LJwrX3m21uPk8u4uO2aCCqCMlmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"885a86742682e610352ff651a05a54cbd0fb975b672d23b7b5423c0732fa7879","last_reissued_at":"2026-05-18T01:25:02.491998Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:02.491998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of action variables near semi-toric singularities","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Christophe Wacheux","submitted_at":"2014-12-07T23:34:53Z","abstract_excerpt":"The presence of focus-focus singularities in semi-toric integrables Hamiltonian systems is one of the reasons why there cannot exist global Action-Angle coordinates on such systems. At focus-focus critical points, the Liouville-Arnold-Mineur theorem does not apply. In particular, the affine structure of the image of the moment map around has non-trivial monodromy. In this article, we establish that the singular behaviour and the multi-valuedness of the Action integrals is given by a complex logarithm. This extends a previous result by Vu Ngoc to any dimension. We also calculate the monodromy m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2414","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.2414","created_at":"2026-05-18T01:25:02.492109+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2414v3","created_at":"2026-05-18T01:25:02.492109+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2414","created_at":"2026-05-18T01:25:02.492109+00:00"},{"alias_kind":"pith_short_12","alias_value":"RBNIM5BGQLTB","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RBNIM5BGQLTBANJP","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RBNIM5BG","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP","json":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP.json","graph_json":"https://pith.science/api/pith-number/RBNIM5BGQLTBANJP6ZI2AWSUZP/graph.json","events_json":"https://pith.science/api/pith-number/RBNIM5BGQLTBANJP6ZI2AWSUZP/events.json","paper":"https://pith.science/paper/RBNIM5BG"},"agent_actions":{"view_html":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP","download_json":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP.json","view_paper":"https://pith.science/paper/RBNIM5BG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2414&json=true","fetch_graph":"https://pith.science/api/pith-number/RBNIM5BGQLTBANJP6ZI2AWSUZP/graph.json","fetch_events":"https://pith.science/api/pith-number/RBNIM5BGQLTBANJP6ZI2AWSUZP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP/action/storage_attestation","attest_author":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP/action/author_attestation","sign_citation":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP/action/citation_signature","submit_replication":"https://pith.science/pith/RBNIM5BGQLTBANJP6ZI2AWSUZP/action/replication_record"}},"created_at":"2026-05-18T01:25:02.492109+00:00","updated_at":"2026-05-18T01:25:02.492109+00:00"}